On the stable solution of large scale problems over the doubly nonnegative cone

The recent approach of solving large scale semidefinite programs with a first order method by minimizing an augmented primal-dual function is extended to doubly nonnegative programs. A key point governing the convergence of this approach are regularity properties of the underlying problem. Regularity of the augmented primal-dual function is established under the condition of uniqueness and strict complementarity. The application to the doubly nonnegative cone is motivated by the fact that the cost per iteration does not increase by adding nonnegativity constraints. Numerical experiments indicate that a two phase approach based on the augmented primal-dual function results in a stable method for solving large scale problems.     

Electronic conductivity of pure ceria

The electronic conductivity of pure ceria with two different impurity levels is examined by dc polarization technique based on the Hebb-Wagner ion blocking method. The impurity level for the ceria with 99.999% purity (5N-CeO₂) is about 1/100 of that with 99.9% purity (3N-CeO₂) as confirmed by the fluorescence intensity of impurities obtained by Raman spectroscopy. The electronic conductivity for the 5N-CeO₂ was measured at T = 973 K to 1173 K, and the results are essentially the same as those for the 3N-CeO₂. The electronic conductivity increases with decreasing of P(O₂) following slope values of − 1/4 to − 1/6. The − 1/4 dependent region becomes narrower for the 5N-CeO₂ than that for the 3N-CeO₂. For both types of ceria, the P(O₂) independent region appears in the same region of higher than 10^− 2 and 10^− 3 MPa at T = 1073 K and 973 K, respectively. Activation energies for the 5N-CeO₂ were 2.2 eV, 2.6 eV and 1.9 eV in P(O₂) dependent regions of − 1/6, − 1/4 and 0, respectively.     

Scaling Solutions of Inelastic Boltzmann Equations with Over-Populated High Energy Tails

This paper deals with solutions of the nonlinear Boltzmann equation for spatially uniform freely cooling inelastic Maxwell models for large times and for large velocities, and the nonuniform convergence to these limits. We demonstrate how the velocity distribution approaches in the scaling limit to a similarity solution with a power law tail for general classes of initial conditions and derive a transcendental equation from which the exponents in the tails can be calculated. Moreover on the basis of the available analytic and numerical results for inelastic hard spheres and inelastic Maxwell models we formulate a conjecture on the approach of the velocity distribution function to a scaling form.     

Towards a Landau–Ginzburg-Type Theory for Granular Fluids

In this paper we show how, under certain restrictions, the hydrodynamic equations for the freely evolving granular fluid fit within the framework of the time dependent Landau–Ginzburg (LG) models for critical and unstable fluids. The granular fluid, which is usually modeled as a fluid of inelastic hard spheres (IHS), exhibits two instabilities: the spontaneous formation of vortices and of high density clusters. We suppress the clustering instability by imposing constraints on the system sizes, in order to illustrate how LG-equations can be derived for the order parameter, being the rate of deformation or shear rate tensor, which controls the formation of vortex patterns. From the shape of the energy functional we obtain the stationary patterns in the flow field. Quantitative predictions of this theory for the stationary states agree well with molecular dynamics simulations of a fluid of inelastic hard disks.     

Molecular simulation of a concentrated aqueous KCl solution

A 1.0 M aqueous KCl solution was studied by molecular dynamics simulations at 293 K in order to study the influence of the ionic concentration on the hydration structure of the ions as well as the formation of ion clusters. The hydration structures of the ions are almost independent of the ionic concentration unless in respect to the perturbation that appears due to ionic clustering. Fractions equal to 31.9% of the anions and 37.8% of the cations are associated. Clusters constituted by two, three and four ions were detected. Their mean lifetimes are always affected by thermal effects, reorientational relaxation while the longest lifetimes are a consequence of ionic cloud relaxations. The pairs constituted by two anions or two cations are stabilized by water molecules belonging to the solvation shells of both ions. The neutral K⁺Cl⁻ pairs are formed under the influence of the electrostatic attraction that, however, is small due to the ionic radii of these ions. Consequently, this kind of pairs contains only 8.8% of the ions while the fraction of ions in the negative and positive pairs are equal to 29.2 and 39.3%, respectively, when the same ion can pertain to more than one pair.     

Picosecond duration laser pulse generation by simultaneous active-passive mode-locking in Ar+ ion and dye lasers

We use a rate equation model to analyse a technique for the generation of picosecond duration laser pulses in argon pumped dye lasers. The system is based on passive mode-locking of the Ar⁺ laser by saturable absorption of the dye which is inserted in the Ar⁺ laser cavity. Simultaneously, the dye is forced to oscillate in a regime of synchronously pumped mode-locking. The system is relatively simple, does not require the use of an acousto-optical light modulator and can be easily implemented in commercially available lasers. Pulses shorter than 100 ps and having an average power of 20 mW were obtained at a repetition rate of 110 MHz. Good agreement between the model and experimental results was also obtained.     

Spontaneous vesicle formation in catanionic mixtures of amino acid-based surfactants: chain length symmetry effects

The use of amino acids for the synthesis of novel surfactants with vesicle-forming properties potentially enhances the biocompatibility levels needed for a viable alternative to conventional lipid vesicles. In this work, the formation and characterization of catanionic vesicles by newly synthesized lysine- and serine-derived surfactants have been investigated by means of phase behavior mapping and PFG-NMR diffusometry and cryo-TEM methods. The lysine-derived surfactants are double-chained anionic molecules bearing a pseudogemini configuration, whereas the serine-derived amphiphile is cationic and single-chained. Vesicles form in the cationic-rich side for narrow mixing ratios of the two amphiphiles. Two pairs of systems were studied: one symmetric with equal chain lengths, 2C12/C12, and the other highly asymmetric with 2C8/C16 chains, where the serine-based surfactant has the longest chain. Different mechanisms of the vesicle-to-micelle transition were found, depending on symmetry: the 2C12/C12 system entails limited micellar growth and intermediate phase separation, whereas the 2C8/C16 system shows a continuous transition involving large wormlike micelles. The results are interpreted on the basis of currently available models for the micelle-vesicle transitions and the stabilization of catanionic vesicles (energy of curvature vs mixing entropy).     

Cluster emission and chemical reactions in oxygen and nitrogen ices induced by fast heavy-ion impact

Two ices, O2 and a mixture of O2 and N2, are bombarded by 252Cf fission fragments (FF) (approximately 65 MeV at target surface); the emitted positive and negative secondary ions are analyzed by time-of-flight mass spectrometry (TOF-SIMS). These studies shall enlighten sputtering from planetary and interstellar ices. Three temperature regions in the 28-42-K range are analyzed: (1) before N2 sublimation, in which hybrid chemical species are formed, (2) before O2 sublimation, in which the TOF mass spectrum is dominated by low-mass (O2)p cluster ions and (3) after O2 sublimation, in which (N2)p or (O2)p cluster ions are practically inexistent. In the first region, four hybrid ion series are observed: NOn-1+, N2On-2(+/-), and N4On-4(-). In the second region, two positive and negative ion series are identified: (O2)pO(+/-) and (O2)pO2(+/-). Their yield distributions are fitted by the sum of two decreasing exponentials, whose decay constants are the same for all series. It is observed that the cluster ion desorption from solid oxygen is very similar to that of other frozen gases, but its yield distribution oscillates with a three- or six-atom periodicity, suggesting O3 or 3O2 units in the cluster structure, respectively.